Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach
Abstract
This paper deals with the linear free vibration analysis of Bernoulli–Euler and Rayleigh curved beams using isogeometric approach. The geometry of the beam as well as the displacement field are defined using the NURBS basis functions which present the basic concept of the isogeometric analysis. A novel approach based on the fundamental relations of the differential geometry and Cauchy continuum beam model is presented and applied to derive the stiffness and consistent mass matrices of the corresponding spatial curved beam element. In the Bernoulli–Euler beam element only translational and torsional inertia are taken into account, while the Rayleigh beam element takes all inertial terms into consideration. Due to their formulation, isogeometric beam elements can be used for the dynamic analysis of spatial curved beams. Several illustrative examples have been chosen in order to check the convergence and accuracy of the proposed method. The results have been compared with the available da...ta from the literature as well as with the finite element solutions.
Keywords:
Bernoulli�Euler theory / Isogeometric analysis / Linear free vibration analysis / Rayleigh theory / Spatial curved beamSource:
Applied Mathematical Modelling, 2019, 71, 152-172Publisher:
- Elsevier Inc.
Funding / projects:
- Development and application of scientific methods in designing and building highly economical structural system using new technologies (RS-36008)
- Towards development of sustainable cities: influence of traffic induced vibrations on buildings and humans (RS-36046)
DOI: 10.1016/j.apm.2019.02.002
ISSN: 0307-904X
WoS: 000468259900010
Scopus: 2-s2.0-85061832155
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Institution/Community
GraFarTY - JOUR AU - Jočković, Miloš AU - Radenković, Gligor AU - Nefovska-Danilović, Marija AU - Baitsch, M. PY - 2019 UR - https://grafar.grf.bg.ac.rs/handle/123456789/986 AB - This paper deals with the linear free vibration analysis of Bernoulli–Euler and Rayleigh curved beams using isogeometric approach. The geometry of the beam as well as the displacement field are defined using the NURBS basis functions which present the basic concept of the isogeometric analysis. A novel approach based on the fundamental relations of the differential geometry and Cauchy continuum beam model is presented and applied to derive the stiffness and consistent mass matrices of the corresponding spatial curved beam element. In the Bernoulli–Euler beam element only translational and torsional inertia are taken into account, while the Rayleigh beam element takes all inertial terms into consideration. Due to their formulation, isogeometric beam elements can be used for the dynamic analysis of spatial curved beams. Several illustrative examples have been chosen in order to check the convergence and accuracy of the proposed method. The results have been compared with the available data from the literature as well as with the finite element solutions. PB - Elsevier Inc. T2 - Applied Mathematical Modelling T1 - Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach EP - 172 SP - 152 VL - 71 DO - 10.1016/j.apm.2019.02.002 ER -
@article{ author = "Jočković, Miloš and Radenković, Gligor and Nefovska-Danilović, Marija and Baitsch, M.", year = "2019", abstract = "This paper deals with the linear free vibration analysis of Bernoulli–Euler and Rayleigh curved beams using isogeometric approach. The geometry of the beam as well as the displacement field are defined using the NURBS basis functions which present the basic concept of the isogeometric analysis. A novel approach based on the fundamental relations of the differential geometry and Cauchy continuum beam model is presented and applied to derive the stiffness and consistent mass matrices of the corresponding spatial curved beam element. In the Bernoulli–Euler beam element only translational and torsional inertia are taken into account, while the Rayleigh beam element takes all inertial terms into consideration. Due to their formulation, isogeometric beam elements can be used for the dynamic analysis of spatial curved beams. Several illustrative examples have been chosen in order to check the convergence and accuracy of the proposed method. The results have been compared with the available data from the literature as well as with the finite element solutions.", publisher = "Elsevier Inc.", journal = "Applied Mathematical Modelling", title = "Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach", pages = "172-152", volume = "71", doi = "10.1016/j.apm.2019.02.002" }
Jočković, M., Radenković, G., Nefovska-Danilović, M.,& Baitsch, M.. (2019). Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach. in Applied Mathematical Modelling Elsevier Inc.., 71, 152-172. https://doi.org/10.1016/j.apm.2019.02.002
Jočković M, Radenković G, Nefovska-Danilović M, Baitsch M. Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach. in Applied Mathematical Modelling. 2019;71:152-172. doi:10.1016/j.apm.2019.02.002 .
Jočković, Miloš, Radenković, Gligor, Nefovska-Danilović, Marija, Baitsch, M., "Free vibration analysis of spatial Bernoulli–Euler and Rayleigh curved beams using isogeometric approach" in Applied Mathematical Modelling, 71 (2019):152-172, https://doi.org/10.1016/j.apm.2019.02.002 . .